How Do I Perform ANOM Normal Two-Way in Excel Using SigmaXL?

We will look at two balanced examples from the ANOM book
(used with author permission),
one with no interaction and another with a strong interaction,
and then a slightly unbalanced
version of the latter (Wludyka, 2013).

Open ANOM Examples.xlsx, click on
Hemoglobin – Normal tab. This data is from a factorial
design to study hemoglobin levels in males (Example 5.1). The factors are
Therapy (Chemo or
Radiation) and Drug (Type 1, 2, 3).
Ensure that the entire data table is selected. If not, check Use Entire Data
Table.

Since the Interaction is not significant (P-Value is >= 0.1),
the Main Effects charts are
highlighted. The decision limits match the manual calculations
given in the ANOM book (pages
87, 88). Since the average hemoglobin level for radiation falls
below the lower decision limit,
and the average for chemotherapy falls above the upper decision
limit, therapy has an (α =
0.05) effect. There is also an effect on hemoglobin level due to
the drug since the average
hemoglobin level for drug 3 is above the upper decision line.

Tip: Two-Way ANOM Normal is complimentary to Two-Way ANOVA.
Analyzing the above data
using Two-Way ANOVA shows that Therapy is significant with a
P-Value = 0.0001, Drug is also
significant with a P-Value = 0.0105 and the Interaction is not
significant, with a P-Value =
0.5942.

This will apply a Bonferroni correction to the specified alpha
values to control the overall
family-wise error rate for the charts. So, the Main Effects
alpha will be = 0.05/2 = 0.025 and the
Slice Charts alpha will be = 0.05/2 = 0.025 as well.

With the Bonferroni corrected alpha of 0.025, the significant
results do not change, but they are
closer to the decision lines. The trade-off for this chart
family-wise adjustment is loss of power.

In ANOM Examples.xlsx, click on Process
Yield – Normal tab. This data is from a factorial
design to study the effect of three monomers and two levels of
UV exposure (1 = UV; 2 = No
UV) on the percent yield for contact lens production (Example
5.3).

Since the Interaction P-Value is < 0.1, the Slice charts are
highlighted. The decision limits for
the Slice charts match the calculations given in Wludyka (2013).
See Appendix References for
Analysis of Means (ANOM) Charts. The Slice plot clearly shows
the effect of the strong
interaction. When UV = 1 (UV Exposure), the three monomers
differ. In particular, the average
for monomer 1 is below the overall average and the average for
monomer 3 is above the
overall average. However, for UV = 2 (no UV), the monomers also
differ but in an entirely
different manner than in the UV = 1 case, revealing the nature
of the interaction.

Tip: As previously noted, Two-Way ANOM Normal
is complimentary to Two-Way ANOVA. Analyzing the above data
using Two-Way ANOVA shows that UV is significant with a P-Value
= 0.0001, Monomer is significant with a P-Value = 0.0000 (4.4
e-5) and the Interaction is also
significant, with P-Value = 0.0000 (2.2e-6).

In ANOM Examples.xlsx, click on Process Yield –
Normal Unbal tab. This data is from a factorial design to study
the effect of three monomers and two levels of UV exposure (1 =
UV; 2
= No UV) on the percent yield for contact lens production, but
two of the observations are
missing for A = 2 (no UV) and B = 3 (monomer 3).

The significant results of the experiment have not changed, but
the decision limits are now
varying due to the unbalanced data and use critical values for
unbalanced data. The decision
limits for the Slice charts match the calculations given in
Wludyka (2013).